Scalar field quantization on the (2+1)-dimensional black hole background

Abstract

The quantization of a massless conformally coupled scalar field on the 2+1 dimensional Anti de Sitter black hole background is presented. The Green's function is calculated, using the fact that the black hole is Anti de Sitter space with points identified, and taking into account the fact that the black hole spacetime is not globally hyperbolic. It is shown that the Green's function calculated in this way is the Hartle-Hawking Green's function. The Green's function is used to compute T µ ν , which is regular on the black hole horizon, and diverges at the singularity. A particle detector response function outside the horizon is also calculated and shown to be a fermi type distribution. The back-reaction from T µν is calculated exactly and is shown to give rise to a curvature singularity at r = 0 and to shift the horizon outwards. For M = 0 a horizon develops, shielding the singularity. Some speculations about the endpoint of evaporation are discussed. 03.70.+k, 04.50.+h, 97.60.Lf

Strings in the Extended BTZ Spacetime

“…First, as we have stressed, this procedure implicitly chooses a particular state of the system (the Hartle-Hawking state) which may or may not be physically realizable. In particular, it is well known that the one-loop expectation value of the energy-momentum tensor of a free scalar field in this state suffers a divergence at the inner horizon [29]; this is a possible mechanism for excising the regions with closed timelike curves. So one can argue that any classical calculations sensitive to the geometry at the inner horizon are unreliable.…”

Classical super-radiance in Kerr–Newman–anti-de Sitter black holes

“…For the KN-AdS black hole and anti-de Sitter space, infinity is time-like and denoted simply I. Corresponding Penrose diagrams for BTZ black holes in three-dimensional anti-de Sitter space may be found in [6,11,34], and for topological black holes in anti-de Sitter space in [35].…”

“…As well as their classical properties, the behaviour of quantum fields on the BTZ black hole has been extensively studied (see, for example, [7,8,9,10]). One advantage of working in three dimensions is that many of the computational aspects are greatly simplified (for example, it is possible to write the Green's function for a quantum field in the Hartle-Hawking state in closed form [11,12,13]). However, there has been more recent interest in higher-dimensional black holes in anti-de Sitter space, particularly Kerr-Newman-anti-de Sitter (KN-AdS) black holes in various dimensions [14,15,16].…”

Holography of the BTZ black hole, inside and out

“…The smoothness of the quotient geometry is also deceptive, and the singularity well deserves its name once one makes any attempt to physically probe it. After quotienting the lightcones of figure 3, they are comprised of closed lightlike curves where even small (quantum) fluctuations [38,39] can backreact divergently with divergent curvatures, and general considerations imply the breakdown of ordinary (effective) field theory [40]. See [41] for a concise review of these general considerations.…”

“…See [41] for a concise review, and [38,39] for computations of stress-tensor divergences at the BTZ singularity. Similar features have also been studied in string theory (as reviewed in [42].)…”